Britain's two oldest quality dailies – the Times, born 1785, and the Guardian, born 1821 – have been fierce, direct competitors since 1959, when the Guardian dropped Manchester from its title. They almost folded into one through the bleak crises of 1966. They've endured price wars, strike wars, Wapping wars and much more. But, baby, look at them now.

At first glance, perhaps, not much has changed. They both make a loss. They must both count the pennies, cut costs and staff. But beyond the ritual of tough words and tough decisions, something more profound is emerging: a fork in the road that begins to set them on wholly different paths.

Last week, the Guardian celebrated a string of scoops that put it at the heart of American public debate. Its US web columnist, Glenn Greenwald, revealed the existence of a huge National Security Agency secret operation digitally tracking hundreds of millions, innocents and suspects alike. Barack Obama scrambled to attention. TV and newspapers cleared their front pages for the Prism sensation. And the Guardian's US web usage, already up 47% year-on-year, set new records.

The Guardian already has some heady successes to talk about: 12,439,000 monthly UK readers of its digital and print versions combined, more than any other quality paper, plus some 54 million monthly unique browsers taking their online tonic outside Britain. These are big numbers defining bigger ambitions as a global digital force which, one day, may leave the world of printing machines far behind and exist mainly or only in cyberspace. And Greenwald's scoop makes that point absolutely. There is no print version of the daily available in America. The story that made Obama sit up was purely online. Here, you might say, is the foreseeable future happening before our eyes.

But John Witherow, the new editor at the Times (forget all the "acting, temporary" stuff, insisted on by his national directors; it's getting plain silly), has a quite different strategy, laid out for staff last week. Predictably enough, the things most people noted from his speech seemed glum news – 20 more editorial jobs axed, costs trimmed again, the imperative to break even in a divided, frailer Murdoch world. But actually, for all the gloom, Witherow's message was surprisingly mild. There will be no meaningful integration between the Times and Sunday Times. The Sunday, breaking back into profit, needs continuing resources to stay strong, he says. Crucial new staff hirings won't be blocked. There is a determination "to make the Times safe, not only for the next few years, but for the foreseeable future".

And though investment and effort will go into tablets, smartphones, subscriptions and the rest, the old fires of print competition still burn. Witherow took a sideswipe at papers whose "sales are falling by up to 10% a year while giving away their content free online". (No wild guesses required.) The subediting changes he's making still revolve around print production. And his boast that "some year-on-year sales are increasing" almost embraces the Times's ABC-audited headline sale, down a mere 0.19% in May to 394,982 a day (as against the Guardian's 192,376).

Of course, it's possible to object that the Times figure includes 18,000 foreign copies and 18,000 bulk giveaways, two padding gambits the Guardian has abandoned. But that means Witherow can sell physical copies in Europe and use a few bulks to increase sampling: which in turn gives the print circulation figure higher salience. More significantly, the Times (at £1 a copy and £1.50 on Saturdays) is substantially cheaper than the Guardian, Telegraph or even Indie. In short, it's trading lost cash for stronger sales, but putting a subscription premium on digital access, while the Guardian is charging customers more but giving its web wares away free. This is a two-way price war on separate battlefields.

So one foreseeable future includes many more dead trees than the other. One still needs ink and deadlines – and the fatter rates that print advertising can command. The other is going for growth around a world where news travels fast. The old hand-to-hand combat is fading.

Now there are huge imponderables all around. Can the Guardian boost revenues to match its ambitions? Is Times life in its subsidy-denuded state any more certain than the last or the next Rupert marriage? Nevertheless, it isn't axiomatically a case of which historic operation can survive any longer. One tentative answer after this month's upheavals might just be: both.